Adaptive noise canceling is a method for estimating the true value/nature of signals that are corrupted by additive noise or interference. In some approaches, a “primary” input {tilde over (s)}=s+n0 is the corrupted signal, and a “reference” input n1 containing noise correlated in some unknown way with the primary noise n0 is a reference signal. The reference input can be adaptively filtered through a finite impulse response (FIR) structure/filter that is defined by a weight column vector w. The filter output can be subtracted from the primary input to obtain the signal estimate. In this manner, adaptive filtering before subtraction can allow for the treatment of inputs that are deterministic or stochastic, stationary or time variable.
Many adaptive techniques have been proposed, such as least mean squares and its variations normalized least mean squares, recursive least squares and variable step least mean squares. Recently, Kalman filters has been employed for this purpose, including, conventional Kalman filtering, fixed-lag smoothing and fixed-interval smoothing. Lee et al. (Physiol. Meas. 31 (2010), 1585-1603) demonstrated a Kalman smoother for eliminating motion artifacts from a photoplethysmography signal. Existing approaches, however, suffer from limited adaptivity and lag error.
Thus, a need exists for systems, apparatuses and methods for adaptive noise reduction with enhanced adaptivity and reduced/no lag error.